PySensors is a Scikit-learn style Python package for the sparse placement of sensors, either for reconstruction or classification tasks.
Table of contents
Sparse sensor placement concerns the problem of selecting a small subset of sensor or measurement locations in a way that allows one to perform some task nearly as well as if one had access to measurements at every location.
PySensors provides objects designed for the tasks of reconstruction and classification. See Manohar et al. (2018) for more information about the PySensors approach to reconstruction problems and Brunton et al. (2016) for classification. de Silva et al. (2021) contains a full literature review along with examples and additional tips for using PySensors effectively.
Reconstruction deals with predicting the values of a quantity of interest at different locations other than those where sensors are located. For example, one might predict the temperature at a point in the middle of a lake based on temperature readings taken at various other positions in the lake.
PySensors provides the SSPOR (Sparse Sensor Placement Optimization for Reconstruction) class to aid in the solution of reconstruction problems.
Take representative examples of the types of data to be reconstructed (in this case polynomials)
x = numpy.linspace(0, 1, 1001)
data = numpy.vander(x, 11).T # Create an array whose rows are powers of xfeed them to a SSPOR instance with 10 sensors, and
model = pysensors.reconstruction.SSPOR(n_sensors=10)
model.fit(data)Use the predict method to reconstruct a new function sampled at the chosen sensor locations:
f = numpy.abs(x[model.selected_sensors]**2 - 0.5)
f_pred = model.predict(f)
In most engineering applications, certain areas within the region of interest might allow a limited number of sensors or none at all. We develop a data-driven technique that incorporates constraints into an optimization framework for sensor placement, with the primary objective of minimizing reconstruction errors under noisy sensor measurements.
This work has been implemented in the general QR optimizer for sensor selection. This is an extension that requires a more intrusive access to the QR optimizer to facilitate a more adaptive optimization. It is a generalized version of cost constraints in the sense that users can allow n_const_sensors in the constrained area. If n = 0 this converges to the CCQR results. If there is no constrained region it should converge to the results from QR optimizer.
To implement constrained sensing we initialize the optimizer GQR and provide it additional kwargs such as the constrained region, number of allowable sensors in the constrained region and the type of constraint.
Three strategies to deal with constraints are currently developed:
max_n- Number of sensors in the constrained region should be less than or equal to the allowable constrained sensors.exact_n- Number of sensors in the constrained region should be exactly equal to the allowable constrained sensors.predetermined- A number of sensor locations are predetermined and the aim is to optimize the rest.
optimizer_exact = ps.optimizers.GQR()
opt_exact_kws={'idx_constrained':sensors_constrained,
'n_sensors':n_sensors,
'n_const_sensors':n_const_sensors,
'all_sensors':all_sensors,
'constraint_option':"exact_n"}We have further provided functions to compute the sensors in the constrained regions. For example if the user provides the center and radius of a circular constrained region, the constraints in utils compute the constrained sensor indices. Direct constraint plotting capabilities have also been developed.
The constrained shapes currently implemented are:
CircleCylinderLineParabolaEllipsePolygonUserDefinedConstraints- This type of constraint has the ability to take in either a function from the user or a
.py file which contains a functional definition of the constrained region.
Classification is the problem of predicting which category an example belongs to, given a set of training data (e.g. determining whether digital photos are of dogs or cats).
The SSPOC (Sparse Sensor Placement Optimization for Classification) class is used to solve classification problems.
Users familiar with Scikit-learn will find it intuitive:
model = pysensors.classification.SSPOC()
model.fit(x, y) # Learn sensor locations and fit a linear classifier
y_pred = model.predict(x_test[:, model.selected_sensors]) # Get predictionsSee our set of classification examples for more information.
The basis in which measurement data are represented can have a dramatic
effect on performance. PySensors implements the three bases most commonly
used for sparse sensor placement: raw measurements, SVD/POD/PCA modes, and random projections. Bases can be easily incorporated into SSPOR and SSPOC classes:
basis = pysensors.basis.SVD(n_basis_modes=20)
recon_model = pysensors.reconstruction.SSPOR(basis=basis)
class_model = pysensors.classification.SSPOC(basis=basis)See this example for further discussion of these options.
The high-level dependencies for PySensors are Linux or macOS and Python 3.6-3.8. pip is also recommended as is makes managing PySensors' other dependencies much easier. You can install it by following the instructions here.
PySensors has not been tested on Windows.
If you are using Linux or macOS you can install PySensors with pip from the command line/terminal:
pip install python-sensorsNote: the name you type in here is python-sensors and is not pysensors.
Once you have run the line above, you are ready to get started with PySensors. Have a look at the examples in our documentation to see what PySensors can do.
First clone this repository:
git clone https://github.com/dynamicslab/pysensors.gitThen, to install the package, run
cd pysensors
pip install .If you do not have pip you can instead use
python setup.py installIf you do not have root access, you should add the --user option to the install commands above.
The primary PySensors objects are the SSPOR and SSPOC classes, which are used to choose sensor locations optimized for reconstruction and classification tasks, respectively. Other implemented objects include
basis- submodule implementing different bases in which to represent dataIdentity- use raw measurement dataSVD- efficiently compute first k left singular vectorsRandomProjection- Gaussian random projections of measurements
- Convenience functions to aid in the analysis of error as number of sensors or basis modes are varied
PySensors has a documentation site hosted by readthedocs.
Examples are available online, as static
Jupyter notebooks and as interactive notebooks. To run the example notebooks locally you should install the dependencies in requirements-examples.txt:
pip install -r requirements-examples.txtYou may create an issue for any questions that aren't answered by the documentation or examples.
If you have used PySensors to solve an interesting problem, please consider submitting an example Jupyter notebook showcasing your work!
We welcome contributions to PySensors. To contribute a new feature please submit a pull request. To get started we recommend installing the packages in requirements-dev.txt via
pip install -r requirements-dev.txtThis will allow you to run unit tests and automatically format your code. To be accepted your code should conform to PEP8 and pass all unit tests. Code can be tested by invoking
pytestWe recommend using pre-commit to format your code. Once you have staged changes to commit
git add path/to/changed/file.pyyou can run the following to automatically reformat your staged code
pre-commitNote that you will then need to re-stage any changes pre-commit made to your code.
If you find a bug in the code or want to request a new feature, please open an issue.
We have published a short paper in the Journal of Open Source Software (JOSS). You can find the paper here.
If you use PySensors in your work, please consider citing it using:
de Silva et al., (2021). PySensors: A Python package for sparse sensor placement. Journal of Open Source Software, 6(58), 2828, https://doi.org/10.21105/joss.02828``
Bibtex:
@article{de Silva2021,
doi = {10.21105/joss.02828},
url = {https://doi.org/10.21105/joss.02828},
year = {2021},
publisher = {The Open Journal},
volume = {6},
number = {58},
pages = {2828},
author = {Brian M. de Silva and Krithika Manohar and Emily Clark and Bingni W. Brunton and J. Nathan Kutz and Steven L. Brunton},
title = {PySensors: A Python package for sparse sensor placement},
journal = {Journal of Open Source Software}
}
de Silva, Brian M., Krithika Manohar, Emily Clark, Bingni W. Brunton, Steven L. Brunton, J. Nathan Kutz. "PySensors: A Python package for sparse sensor placement." arXiv preprint arXiv:2102.13476 (2021). [arXiv]
Manohar, Krithika, Bingni W. Brunton, J. Nathan Kutz, and Steven L. Brunton. "Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns." IEEE Control Systems Magazine 38, no. 3 (2018): 63-86. [DOI]
Brunton, Bingni W., Steven L. Brunton, Joshua L. Proctor, and J Nathan Kutz. "Sparse sensor placement optimization for classification." SIAM Journal on Applied Mathematics 76.5 (2016): 2099-2122. [DOI]
Clark, Emily, Travis Askham, Steven L. Brunton, and J. Nathan Kutz. "Greedy sensor placement with cost constraints." IEEE Sensors Journal 19, no. 7 (2018): 2642-2656. [DOI]
- Karnik, Niharika, Mohammad G. Abdo, Carlos E. Estrada-Perez, Jun Soo Yoo,
Joshua J. Cogliati, Richard S. Skifton, Pattrick Calderoni, Steven L. Brunton, and Krithika Manohar.
"Constrained Optimization of Sensor Plcaement for Nuclear Digital Twins" IEEE Sensors Journal 24, no. 9 (2024): 15501 - 15516. [DOI]